Properties

Label 869.1.j.a.394.1
Level $869$
Weight $1$
Character 869.394
Analytic conductor $0.434$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -79
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 869 = 11 \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 869.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.433687495978\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{50})\)
Defining polynomial: \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{25}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{25} - \cdots)\)

Embedding invariants

Embedding label 394.1
Root \(-0.876307 + 0.481754i\) of defining polynomial
Character \(\chi\) \(=\) 869.394
Dual form 869.1.j.a.236.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.613161 + 1.88711i) q^{2} +(-2.37622 - 1.72642i) q^{4} +(0.0388067 + 0.119435i) q^{5} +(3.10969 - 2.25932i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.613161 + 1.88711i) q^{2} +(-2.37622 - 1.72642i) q^{4} +(0.0388067 + 0.119435i) q^{5} +(3.10969 - 2.25932i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.249182 q^{10} +(-0.992115 - 0.125333i) q^{11} +(0.541587 - 1.66683i) q^{13} +(1.44922 + 4.46025i) q^{16} +(1.60528 + 1.16630i) q^{18} +(1.03137 - 0.749337i) q^{19} +(0.113982 - 0.350799i) q^{20} +(0.844844 - 1.79538i) q^{22} -1.27485 q^{23} +(0.796258 - 0.578516i) q^{25} +(2.81343 + 2.04407i) q^{26} +(-0.263146 + 0.809880i) q^{31} -5.46182 q^{32} +(-2.37622 + 1.72642i) q^{36} +(0.781687 + 2.40578i) q^{38} +(0.390518 + 0.283728i) q^{40} +(2.14110 + 2.01063i) q^{44} +0.125581 q^{45} +(0.781687 - 2.40578i) q^{46} +(0.309017 + 0.951057i) q^{49} +(0.603491 + 1.85735i) q^{50} +(-4.16459 + 3.02575i) q^{52} +(-0.0235315 - 0.123357i) q^{55} +(-1.36699 - 0.993173i) q^{62} +(1.89975 - 5.84683i) q^{64} +0.220095 q^{65} +1.07165 q^{67} +(-1.18779 - 3.65565i) q^{72} +(-1.56720 - 1.13864i) q^{73} -3.74444 q^{76} +(0.309017 - 0.951057i) q^{79} +(-0.476468 + 0.346175i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{83} +(-3.36833 + 1.85176i) q^{88} +1.45794 q^{89} +(-0.0770013 + 0.236986i) q^{90} +(3.02932 + 2.20093i) q^{92} +(0.129521 + 0.0941025i) q^{95} +(-0.574633 + 1.76854i) q^{97} -1.98423 q^{98} +(-0.425779 + 0.904827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/869\mathbb{Z}\right)^\times\).

\(n\) \(475\) \(793\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(3\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) −2.37622 1.72642i −2.37622 1.72642i
\(5\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(6\) 0 0
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) 3.10969 2.25932i 3.10969 2.25932i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) −0.249182 −0.249182
\(11\) −0.992115 0.125333i −0.992115 0.125333i
\(12\) 0 0
\(13\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.44922 + 4.46025i 1.44922 + 4.46025i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(19\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(20\) 0.113982 0.350799i 0.113982 0.350799i
\(21\) 0 0
\(22\) 0.844844 1.79538i 0.844844 1.79538i
\(23\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(24\) 0 0
\(25\) 0.796258 0.578516i 0.796258 0.578516i
\(26\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(32\) −5.46182 −5.46182
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −2.37622 + 1.72642i −2.37622 + 1.72642i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) 0.781687 + 2.40578i 0.781687 + 2.40578i
\(39\) 0 0
\(40\) 0.390518 + 0.283728i 0.390518 + 0.283728i
\(41\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 2.14110 + 2.01063i 2.14110 + 2.01063i
\(45\) 0.125581 0.125581
\(46\) 0.781687 2.40578i 0.781687 2.40578i
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) 0 0
\(49\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(50\) 0.603491 + 1.85735i 0.603491 + 1.85735i
\(51\) 0 0
\(52\) −4.16459 + 3.02575i −4.16459 + 3.02575i
\(53\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 0 0
\(55\) −0.0235315 0.123357i −0.0235315 0.123357i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(62\) −1.36699 0.993173i −1.36699 0.993173i
\(63\) 0 0
\(64\) 1.89975 5.84683i 1.89975 5.84683i
\(65\) 0.220095 0.220095
\(66\) 0 0
\(67\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) −1.18779 3.65565i −1.18779 3.65565i
\(73\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −3.74444 −3.74444
\(77\) 0 0
\(78\) 0 0
\(79\) 0.309017 0.951057i 0.309017 0.951057i
\(80\) −0.476468 + 0.346175i −0.476468 + 0.346175i
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0 0
\(83\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −3.36833 + 1.85176i −3.36833 + 1.85176i
\(89\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(90\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(91\) 0 0
\(92\) 3.02932 + 2.20093i 3.02932 + 2.20093i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.129521 + 0.0941025i 0.129521 + 0.0941025i
\(96\) 0 0
\(97\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(98\) −1.98423 −1.98423
\(99\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(100\) −2.89085 −2.89085
\(101\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) −2.08174 6.40695i −2.08174 6.40695i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0.247217 + 0.0312307i 0.247217 + 0.0312307i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) −0.0494726 0.152261i −0.0494726 0.152261i
\(116\) 0 0
\(117\) −1.41789 1.03016i −1.41789 1.03016i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(122\) 0 0
\(123\) 0 0
\(124\) 2.02349 1.47015i 2.02349 1.47015i
\(125\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(126\) 0 0
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 5.45008 + 3.95971i 5.45008 + 3.95971i
\(129\) 0 0
\(130\) −0.134954 + 0.415344i −0.134954 + 0.415344i
\(131\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.657096 + 2.02233i −0.657096 + 2.02233i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.746226 + 1.58581i −0.746226 + 1.58581i
\(144\) 4.68978 4.68978
\(145\) 0 0
\(146\) 3.10969 2.25932i 3.10969 2.25932i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) 0 0
\(151\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(152\) 1.51426 4.66040i 1.51426 4.66040i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.106940 −0.106940
\(156\) 0 0
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(159\) 0 0
\(160\) −0.211955 0.652330i −0.211955 0.652330i
\(161\) 0 0
\(162\) 1.60528 1.16630i 1.60528 1.16630i
\(163\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.22632 −1.22632
\(167\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(168\) 0 0
\(169\) −1.67600 1.21769i −1.67600 1.21769i
\(170\) 0 0
\(171\) −0.393950 1.21245i −0.393950 1.21245i
\(172\) 0 0
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.878777 4.60671i −0.878777 4.60671i
\(177\) 0 0
\(178\) −0.893950 + 2.75129i −0.893950 + 2.75129i
\(179\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) −0.298408 0.216806i −0.298408 0.216806i
\(181\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.96438 + 2.88029i −3.96438 + 2.88029i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −0.256999 + 0.186721i −0.256999 + 0.186721i
\(191\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(192\) 0 0
\(193\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(194\) −2.98509 2.16880i −2.98509 2.16880i
\(195\) 0 0
\(196\) 0.907634 2.79341i 0.907634 2.79341i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.44644 1.35830i −1.44644 1.35830i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.16906 3.59800i 1.16906 3.59800i
\(201\) 0 0
\(202\) 2.34039 + 1.70039i 2.34039 + 1.70039i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(208\) 8.21937 8.21937
\(209\) −1.11716 + 0.614163i −1.11716 + 0.614163i
\(210\) 0 0
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.157050 + 0.333748i −0.157050 + 0.333748i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(224\) 0 0
\(225\) −0.304144 0.936058i −0.304144 0.936058i
\(226\) 0 0
\(227\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(228\) 0 0
\(229\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(230\) 0.317669 0.317669
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(234\) 2.81343 2.04407i 2.81343 2.04407i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(240\) 0 0
\(241\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(242\) −1.06320 + 1.67534i −1.06320 + 1.67534i
\(243\) 0 0
\(244\) 0 0
\(245\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(246\) 0 0
\(247\) −0.690441 2.12496i −0.690441 2.12496i
\(248\) 1.01148 + 3.11300i 1.01148 + 3.11300i
\(249\) 0 0
\(250\) −0.400005 + 0.290621i −0.400005 + 0.290621i
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 0 0
\(253\) 1.26480 + 0.159781i 1.26480 + 0.159781i
\(254\) 0 0
\(255\) 0 0
\(256\) −5.84059 + 4.24344i −5.84059 + 4.24344i
\(257\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.522994 0.379977i −0.522994 0.379977i
\(261\) 0 0
\(262\) −1.18779 + 3.65565i −1.18779 + 3.65565i
\(263\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −2.54648 1.85013i −2.54648 1.85013i
\(269\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.862487 + 0.474156i −0.862487 + 0.474156i
\(276\) 0 0
\(277\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(278\) 0 0
\(279\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(280\) 0 0
\(281\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(282\) 0 0
\(283\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.53505 2.38057i −2.53505 2.38057i
\(287\) 0 0
\(288\) −1.68779 + 5.19450i −1.68779 + 5.19450i
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.75824 + 5.41130i 1.75824 + 5.41130i
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.657096 2.02233i −0.657096 2.02233i
\(303\) 0 0
\(304\) 4.83692 + 3.51422i 4.83692 + 3.51422i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.0655712 0.201807i 0.0655712 0.201807i
\(311\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0 0
\(313\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −2.37622 + 1.72642i −2.37622 + 1.72642i
\(317\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.772037 0.772037
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.907634 + 2.79341i 0.907634 + 2.79341i
\(325\) −0.533046 1.64055i −0.533046 1.64055i
\(326\) −0.601597 0.437086i −0.601597 0.437086i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.560949 1.72642i 0.560949 1.72642i
\(333\) 0 0
\(334\) −1.36699 0.993173i −1.36699 0.993173i
\(335\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(336\) 0 0
\(337\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(338\) 3.32557 2.41617i 3.32557 2.41617i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.362576 0.770513i 0.362576 0.770513i
\(342\) 2.52959 2.52959
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(348\) 0 0
\(349\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 5.41875 + 0.684547i 5.41875 + 0.684547i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −3.46438 2.51702i −3.46438 2.51702i
\(357\) 0 0
\(358\) −0.378954 1.16630i −0.378954 1.16630i
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) 0.390518 0.283728i 0.390518 0.283728i
\(361\) 0.193209 0.594636i 0.193209 0.594636i
\(362\) −3.47759 −3.47759
\(363\) 0 0
\(364\) 0 0
\(365\) 0.0751750 0.231365i 0.0751750 0.231365i
\(366\) 0 0
\(367\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(368\) −1.84754 5.68613i −1.84754 5.68613i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) −0.145309 0.447216i −0.145309 0.447216i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 4.41870 3.21038i 4.41870 3.21038i
\(389\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.10969 + 2.25932i 3.10969 + 2.25932i
\(393\) 0 0
\(394\) 0 0
\(395\) 0.125581 0.125581
\(396\) 2.57386 1.41499i 2.57386 1.41499i
\(397\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.73428 + 2.71311i 3.73428 + 2.71311i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(404\) −3.46438 + 2.51702i −3.46438 + 2.51702i
\(405\) 0.0388067 0.119435i 0.0388067 0.119435i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −2.04648 1.48686i −2.04648 1.48686i
\(415\) −0.0627905 + 0.0456200i −0.0627905 + 0.0456200i
\(416\) −2.95805 + 9.10394i −2.95805 + 9.10394i
\(417\) 0 0
\(418\) −0.473998 2.48478i −0.473998 2.48478i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(432\) 0 0
\(433\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.31484 + 0.955291i −1.31484 + 0.955291i
\(438\) 0 0
\(439\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(440\) −0.351878 0.330435i −0.351878 0.330435i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0.0565777 + 0.174128i 0.0565777 + 0.174128i
\(446\) −0.378954 1.16630i −0.378954 1.16630i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 1.95294 1.95294
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.145309 + 0.447216i −0.145309 + 0.447216i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(468\) 1.59073 + 4.89577i 1.59073 + 4.89577i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.387737 1.19333i 0.387737 1.19333i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.0770013 0.236986i −0.0770013 0.236986i
\(479\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.229790 0.707220i 0.229790 0.707220i
\(483\) 0 0
\(484\) −1.87222 2.26313i −1.87222 2.26313i
\(485\) −0.233525 −0.233525
\(486\) 0 0
\(487\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.0770013 0.236986i −0.0770013 0.236986i
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 4.43339 4.43339
\(495\) −0.124591 0.0157395i −0.124591 0.0157395i
\(496\) −3.99362 −3.99362
\(497\) 0 0
\(498\) 0 0
\(499\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(500\) −0.226166 0.696067i −0.226166 0.696067i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) 0.183089 0.183089
\(506\) −1.07705 + 2.28884i −1.07705 + 2.28884i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −2.34489 7.21683i −2.34489 7.21683i
\(513\) 0 0
\(514\) 2.81343 2.04407i 2.81343 2.04407i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.684426 0.497265i 0.684426 0.497265i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(524\) −4.60313 3.34437i −4.60313 3.34437i
\(525\) 0 0
\(526\) 0.229790 0.707220i 0.229790 0.707220i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.625237 0.625237
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 3.33251 2.42121i 3.33251 2.42121i
\(537\) 0 0
\(538\) −2.12641 −2.12641
\(539\) −0.187381 0.982287i −0.187381 0.982287i
\(540\) 0 0
\(541\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.365944 1.91835i −0.365944 1.91835i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(558\) −1.36699 + 0.993173i −1.36699 + 0.993173i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.249182 −0.249182
\(563\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.522142 + 1.60699i 0.522142 + 1.60699i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(570\) 0 0
\(571\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(572\) 4.51098 2.47993i 4.51098 2.47993i
\(573\) 0 0
\(574\) 0 0
\(575\) −1.01511 + 0.737519i −1.01511 + 0.737519i
\(576\) −4.97361 3.61354i −4.97361 3.61354i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) −0.613161 1.88711i −0.613161 1.88711i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −7.44605 −7.44605
\(585\) 0.0680131 0.209323i 0.0680131 0.209323i
\(586\) 0 0
\(587\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(588\) 0 0
\(589\) 0.335471 + 1.03247i 0.335471 + 1.03247i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −3.58669 2.60588i −3.58669 2.60588i
\(599\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(602\) 0 0
\(603\) 0.331159 1.01920i 0.331159 1.01920i
\(604\) 3.14762 3.14762
\(605\) 0.00788530 + 0.125333i 0.00788530 + 0.125333i
\(606\) 0 0
\(607\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) −5.63317 + 4.09274i −5.63317 + 4.09274i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(618\) 0 0
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 0.254112 + 0.184623i 0.254112 + 0.184623i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.294474 0.906297i 0.294474 0.906297i
\(626\) 1.68969 1.68969
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) −1.18779 3.65565i −1.18779 3.65565i
\(633\) 0 0
\(634\) −2.59739 1.88711i −2.59739 1.88711i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.75261 1.75261
\(638\) 0 0
\(639\) 0 0
\(640\) −0.261428 + 0.804591i −0.261428 + 0.804591i
\(641\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(642\) 0 0
\(643\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) −3.84378 −3.84378
\(649\) 0 0
\(650\) 3.42274 3.42274
\(651\) 0 0
\(652\) 0.890518 0.646999i 0.890518 0.646999i
\(653\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(654\) 0 0
\(655\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(656\) 0 0
\(657\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.92189 + 1.39634i 1.92189 + 1.39634i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 2.02349 1.47015i 2.02349 1.47015i
\(669\) 0 0
\(670\) −0.267036 −0.267036
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(675\) 0 0
\(676\) 1.88030 + 5.78698i 1.88030 + 5.78698i
\(677\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 1.23173 + 1.15667i 1.23173 + 1.15667i
\(683\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(684\) −1.15710 + 3.56117i −1.15710 + 3.56117i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −2.12641 −2.12641
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −2.61757 + 5.56262i −2.61757 + 5.56262i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) −0.809017 0.587785i −0.809017 0.587785i
\(712\) 4.53373 3.29394i 4.53373 3.29394i
\(713\) 0.335471 1.03247i 0.335471 1.03247i
\(714\) 0 0
\(715\) −0.218359 0.0275852i −0.218359 0.0275852i
\(716\) 1.81527 1.81527
\(717\) 0 0
\(718\) 0 0
\(719\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(720\) 0.181995 + 0.560122i 0.181995 + 0.560122i
\(721\) 0 0
\(722\) 1.00368 + 0.729215i 1.00368 + 0.729215i
\(723\) 0 0
\(724\) 1.59073 4.89577i 1.59073 4.89577i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) 0.390518 + 0.283728i 0.390518 + 0.283728i
\(731\) 0 0
\(732\) 0 0
\(733\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(734\) 2.34039 1.70039i 2.34039 1.70039i
\(735\) 0 0
\(736\) 6.96299 6.96299
\(737\) −1.06320 0.134314i −1.06320 0.134314i
\(738\) 0 0
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.618034 0.618034
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.108877 0.0791038i −0.108877 0.0791038i
\(756\) 0 0
\(757\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.615377 0.615377
\(761\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −3.18523 2.31421i −3.18523 2.31421i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(774\) 0 0
\(775\) 0.258996 + 0.797108i 0.258996 + 0.797108i
\(776\) 2.20877 + 6.79788i 2.20877 + 6.79788i
\(777\) 0 0
\(778\) −1.36699 + 0.993173i −1.36699 + 0.993173i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −3.79411 + 2.75658i −3.79411 + 2.75658i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(791\) 0 0
\(792\) 0.720253 + 3.77570i 0.720253 + 3.77570i
\(793\) 0 0
\(794\) −0.378954 + 1.16630i −0.378954 + 1.16630i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −4.34902 + 3.15975i −4.34902 + 3.15975i
\(801\) 0.450527 1.38658i 0.450527 1.38658i
\(802\) 0 0
\(803\)